GIST is held Fridays from 3:15-4:15 in Maloney 560!

September 1, 2023: Introduction and Social

September 8, 2023: Laura Seaberg

Title: The Quest for the Aperiodic Monotile 

Abstract: There are only a few times that a mathematical discovery makes it to mainstream news (and when it does, it's often a new prime number). But this spring, another discovery hit the presses--an aperiodic monotile, or a single shape which tiles the plane but only in ways forbidding translational symmetry. This talk will summarize the history of aperiodic tilings and indicate some key techniques used in the preprint by Smith, Myers, Kaplan, and Goodman-Strauss. No prerequisites are assumed and we will look at plenty of pictures. As two tiles named "the hat" and "the specter" will be featured, you are invited to either wear your favorite hat or dress up as a ghost. 

September 15, 2023: Yaoying Fu

Title: A bit of Ramsey theory 

Abstract: In the 1960's, Sándor Szalai studied relationships between children. He discovered that in any class of about 20 children, he always found either four children, any pair of whom knew each other or four children, no pair of whom knew one another. He suspected this was a mathematical phenomenon. He contacted Paul Erdős, Vera Sós and Paul Turán, who explained that it was an instance of a theorem in Ramsey theory. In this talk, we will have fun with a bit of Ramsey theory. There's no prerequisite required at all, as long as you have an idea of how to draw a graph consisting of edges and vertices >.< 

September 22, 2023: Mira Wattal

Title: A group with an inferiority complex

Abstract: This talk will be centered on the two banes of the author’s existence: petiteness and counting. Unfortunately for her, we will study the structure of the group associated with the petite (2 x 2 x 2) Rubik’s cube, the “miniature Rubik’s group”. Despite its shortcomings, the author takes solace in the fact that this miniature group has at least 29,160 elements that she didn’t have to count (at least not one by one).  

September 29, 2023: Board Game Social Hour

October 6, 2023: Fall Break- NO GIST

October 13, 2023: Eric Moss

Title: Some Connections Between Domains and Domains

Abstract: A discrete action of Mobius transformations has a fundamental domain. If our group of actions is defined over a domain (I really mean a ring of integers), then properties of the ring-theoretic domain appear in the fundamental domain. We’ll do a deep dive into the case of Z, into a Mobius action coming from imaginary quadratic fields, and into what a noneuclidean domain really means. No number theory knowledge is required! 

October 20, 2023: Joaquin Lema

Title: Real projective manifolds

Abstract: One of the first times I fell in love with math was attending a classical projective geometry course. I'll try to show my love for the subject by telling you how we use it nowadays to geometrize manifolds and how the richness of projective geometry lets us do so much with so little. The talk will be open-ended, so I'd love it if you interrupt me and stir the conversation towards something you find beautiful. 

October 27, 2023: Pumpkin Carving Event!

November 3, 2023: Matt Zevenbergen

Title: Fully Augmented Links

Abstract: Okay, so I'm gonna talk about hyperbolic geometry. But I promise it's gonna be really fun. There's gonna be lots of pictures. This talk is gonna have the full hodgepodge of fun geometry objects: links, circle packings, polyhedra, graphs, the works. I'll introduce a really nice family of hyperbolic links called fully augmented links, and we'll talk about why they're hyperbolic. There won't be any real geometry knowledge needed. 

November 10, 2023: Miguel Prado

Title: Galois groups on enumerative problems

Abstract: Enumerative problems can often be expressed as a finite morphism of algebraic varieties. This morphism has two groups associated to them, one is the Galois group of the function fields of the varieties and the second is the monodromy group created by how the fundamental group in the image interchanges the fibers over the base point. These two groups are the same and the information of each group gives describes interesting structures about the geometry of the problem and how we can compute the solutions. I'll go through specific examples.

November 17, 2023: Ali Naseri Sadr

Title: Let's do some analysis!

Abstract: Before coming to BC, I was an analyst and I miss doing analysis. That is why I decided to talk about some of the stuff I learnt back then. I am gonna start by telling you about Hilbert's 19th problem and introducing a general setting for calculus of variations and regularity theory. Then I will tell you what Elliptic Regularity is and how De Giorgi and Nash proved it 60 years ago. Since then, Elliptic Regularity has played an important role in PDE theory and other areas of math. 

November 24, 2023: Thanksgiving Break- NO GIST

December 1, 2023: Arieh Zimmerman

Title: Reppin' for Rep Theory

Abstract: We'll use spherical harmonics to prove that any centrally symmetric convex body can be reconstructed by knowing the area of each of its cross-sections. I'll lead into it with an overview of the representation theory of SO_3, showing the relevance of the Laplacian and harmonic polynomials.

December 8, 2023: Gage Martin

Title: An Unexpected Application

Abstract: Structuralism was an influential academic framework and its impacts are still evident in contemporary society. The anthropologist Claude Lévi-Strauss played a key role in moving structuralism from a linguistic theory to the forefront of academic thought. Recently I was surprised to learn that one of his first influential structuralist works involves a non-trivial application of mathematics. In this talk I will explain this application and give context for why I find this fascinating.